Regularization Method for Nonlinear Singularly Perturbed Systems of Fractional Order


  • Burkhan Kalimbetov Akhmed Yasawi University
  • Riskeldy Turgunbaev



Nonlinear differential equation of fractional order, regularization, asymptotic, iteration problems, normal and unique solvability, computer mathematics system Maple.


The paper is devoted to construction of an asymptotic solution of a weakly nonlinear singularly perturbed differential system of fractional order. To construct the asymptotic solution we use ideas of normal differential forms method of V.F. Safonov. In the environment of the computer mathematical system Maple, approximate solutions are calculated, and corresponding solution schedules for various values of a small parameter are constructed.


Safonov, V.F. (1987) Multipoint resonance in a strongly nonlinear singularly perturbed system of differential equations. J. Differential Equations, 3, 529–530.

Safonov, V.F. (1989) Normal forms and regularization of nonlinear singularly perturbed evolution equations. J. Differential Equations, 25, 627–635.

Safonov, V.F. (1979) Regularization method for singularly perturbed systems of nonlinear differential equations. Izv. AS of USSR. Ser. mathem., 43, (3), 628–653.

Kalimbetov B.Т. (2007) Algorithm of method of normal forms for a weakly nonlinear equation with an unstable spectrum. Uzbek. Mathem. Journal, 2, 56–69.

Kalimbetov, B.Т. and Safonov, V.F. (1989) Normalized asymptotic solutions of weakly nonlinear singularly perturbed Cauchy problem with an unstable spectrum. Research on Integro-Differential. Equation, Frunze: "Ilim", 22, 37-42.

Dyakonov, V.P. Maple 7. Training Course. St. Petersburg, "Peter", 2003.

Kirsanov, M.N. Graphs in Maple. Moscow, Fizmathlit, 2007.




How to Cite

Kalimbetov, B., & Turgunbaev, R. (2018). Regularization Method for Nonlinear Singularly Perturbed Systems of Fractional Order. Asian Journal of Fuzzy and Applied Mathematics, 6(3).